The Man-Kzin wars series are shared-world anthology books - basically, lots of different authors wrote short stories and novellas ( with wildly-varying quality) using the Nivenverse... You won't really be missing out on much if you give them a miss.
"Wildly varying quality", I agree. "Won't miss out much", I disagree, especially if you like the Kzin. There is much more meat put on the bones of their culture (much like later series of Star Trek did for the (originally one-dimensional) Klingons.) There are also some excellent stories and first rate writers involved -
The Captain's Tiger has a British Army officer in Victorian India on Earth meeting a Kzin. Some of the stories are arguably apocryphal while still good -
A Darker Geometry was one about the origin of the Outsiders.
The Wunder War - is about the human resistance fighters on Wunderland and more meat is put on the bones of these earth colonies too.
I would read the Man-Kzin Wars series after other books. Some may also be out of print. They were originally published by Baen Books at about one per year, but the better volumes were then reprinted again later and it looks like there have been further reprints and different editions.
As for the order of reading the original Known Space short stories, I'd be tied between advising reading in the order they were written, against their order in the timeline. Some of the earliest stories i.e. The Coldest Place about Pluto have been superseded by scientific discovery. Also, the short-story compilations that I own are no longer in print and the new compilations have different selections of stories in different orders.
I also enjoyed reading the more recent series,
The World of... series with Edward M. Lerner which cleverly integrates the original short stories into much longer stories, filling in the gaps as it does so, and adding additional layers to the plots. Even if you can get hold of the original short stories, this might be a preferable way to read them.
As for Larry Niven's other work, be sure to read the Svetz time-travel series and the Magic Goes Away fantasy series too.
